Finding MAPs using strongly equivalent high order recurrent symmetric connectionist networks

Belief revision is the problem of finding the most plausible explanation for an observed set of evidences. It has many applications in various scientific domains like natural language understanding, medical diagnosis and computational biology. Bayesian Networks (BN) is an important probabilistic graphical formalism widely used for belief revision tasks. In BN, belief revision can be achieved by finding the maximum a posteriori (MAP) assignment. Finding MAP is an NP-Hard problem. In previous work, we showed how to find the MAP assignment in BN using High Order Recurrent Neural Networks (HORN) through an intermediate representation of Cost-Based Abduction. This method eliminates the need to explicitly construct the energy function in two steps, objective and constraints. This paper builds on that previous work by providing the theoretical foundation and proving that the resultant HORN used to find MAP is strongly equivalent to the original BN it tries to solve.